#6 - Number Sense
STATE GOAL 6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
Why This Goal Is Important: Numbers and operations on numbers play fundamental roles in helping us make sense of the world around us. Operations such as addition, subtraction, multiplication and division, as well as the ability to find powers and roots, extend the notion of numbers to create tools to model situations and solve problems in our everyday lives. Discussing and solving problems related to budgets, comparing prices on merchandise, understanding the nature of interest charges, measuring fuel consumption and calculating the trajectory for space travel would all be impossible without a sense of numbers and numerical operations. All people must develop this sense of numbers and operations and be able to use it to solve problems using mental computation, paper-and-pencil algorithms, calculators and computers.
Illinois Mathematics Standards covered: ( 6A, 6C, & 6D ) .
Learning Standard 6A. Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings. Early Elementary 6.A.1a Identify whole numbers and compare them using the symbols <, >, or = and the words "less than", "greater than", or "equal to", applying counting, grouping and place value concepts. Late Elementary 6.A.2 Compare and order whole numbers, fractions and decimals using concrete materials, drawings and mathematical symbols. Middle & Junior
6.A.3 Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. Early High School 6.A.4 Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots. Late High School 6.A.5 Perform addition, subtraction and multiplication of complex numbers and graph the results in the complex plane. Learning Standard 6C. Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers. Early Elementary 6.C.1a Select and perform computational procedures to solve problems with whole numbers. Early Elementary 6.C.1b Show evidence that whole number computational results are correct and/or that estimates are reasonable. Late Elementary 6.C.2a Select and perform computational procedures to solve problems with whole numbers, fractions and decimals Late Elementary 6.C.2b Show evidence that computational results using whole numbers, fractions and decimals are correct and/or that estimates are reasonable. Middle & Junior
6.C.3a Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions. Middle & Junior
6.C.3b Show evidence that computational results using whole numbers, fractions, decimals, percents and proportions are correct and/or that estimates are reasonable. Early High School 6.C.4 Determine whether exact values or approximations are appropriate (e.g., bid a job, determine gas mileage for a trip). Late High School 6.C.5 Determine the level of accuracy needed for computations involving measurement and irrational numbers. Learning Standard 6D. Solve problems using comparison of quantities, ratios, proportions and percents. Early Elementary 6.D.1 Compare the numbers of objects in groups. Late Elementary 6.D.2 Describe the relationship between two sets of data using ratios and appropriate notations (e.g., a/b, a to b, a:b). Middle & Junior
6.D.3 Apply ratios and proportions to solve practical problems. Early High School 6.D.4 Solve problems involving recipes or mixtures, financial calculations and geometric similarity using ratios, proportions and percents. Late High School 6.D.5 Solve problems involving loans, mortgages and other practical applications involving geometric patterns of growth.
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